More budget never removes effort. An Evidence Press briefing. Many planning problems share one simple shape. Think of mosquito larvae, crop pests, people waiting to be vaccinated, or a harvested fish stock. A stock is refilled by a seasonal inflow, decays naturally, and is reduced by effort that removes a share of it, either steadily or in short pulses. With a fixed amount of effort each year, the planner wants the lowest seasonally weighted average stock. Gavish and Katriel worked out what the best plans look like, and conjectured that a bigger budget never makes it optimal to do less at any time of year. That is not obvious, because effort early in the year lowers the stock later, so extra money might in principle be better spent by moving effort between seasons. This release proves the conjecture in the form the authors describe in words. In their model, when the yearly budget rises, the optimal effort in every part of the year can only stay the same or grow. Treated seasons are nested, and no pulse ever gets smaller. So plans can be built step by step: if the budget goes up, add to the existing plan, and nothing already scheduled needs to be cancelled. The paper also shows where this stops. It survives limits on how much can be done at once. It can fail when effort is cheaper, or works better, in some seasons than in others; then extra budget can make it optimal to shrink one round. With fixed treatment dates, it can also fail when the cost of the stock is not proportional to its size. And if the budget counts doses rather than the share removed, the problem changes character, and the best plan is often a single campaign. A related conjecture by the same authors, about the timing of seasonal vaccination, also follows, apart from a narrow technical exception. The practical advice is to fix the unit of the budget first, and to check whether prices or efficacy vary with the season. These are mathematical results about a simple model, not field evidence. This is an anonymous, AI-assisted, unrefereed candidate, not peer reviewed or independently reproduced. Published on 21 October 2026, its paper and evidence are linked from the Evidence Press release page. This briefing uses an AI-generated voice and is not additional scientific evidence.